Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Electrical and Computer Engineering


Electrical Engineering

First Advisor

John R. Bowler


Since 1950s sodium cooled fast reactors (SFR) have been developed and have been approaching their commercialization as nuclear power plants through the development of experimental and prototype reactors. High-performance steels such as 9Cr-1Mo, oxide dispersion strengthened (ODS) have been used for metallic parts such as heat exchanger tubes and fuel cladding in fast reactors. They are favored because of their high temperature creep and fatigue resistance properties. Periodical nondestructive in-service inspection (ISI) of those metallic parts is essential since any damage in the parts can lead to malfunction or even destructive accidents. However, most of the numerical and theoretical models are developed for non-magnetic materials. In this dissertation, theoretical and computational approaches are proposed to solve eddy current problems for both ferromagnetic and non-ferromagnetic conductors.

By applying the volume equivalence theorem, the effects of a flaw in the conductor are represented by an equivalent electric current dipole density and a magnetic dipole density. Volume integral equations are then derived for multi-layered structures. The general dyadic Green's kernels dedicated to a layered geometry are derived here based on a decomposition of the electromagnetic field into a transverse electric scalar potential and a transverse magnetic scalar potential. The dyadic Green's kernels for either planar-layered or cylindrical-layered structures can be derived from the corresponding scalar kernels.

The dedicated dyadic Green's kernels for a conductive half-space and slab are derived and discussed. Naturally, the method of moments (MoM) is used to obtain the numerical approximation of the integral equations. The incident field, also known as the unperturbed field, plays a important role in the method of moments and is determined in Chapter 4, 7 and Chapter 8. For better accuracy and calculation efficiency, a simple analytical method for evaluating the hyper-singular element is provided for the matrix component calculation and validated by calculating the radar cross-section (RCS) of dielectric sphere.

Experiments are carried out to obtain the impedance variation of a circular coil probe due to narrow notches in a ferromagnetic steel slabs (440 stainless steel) for comparison with theoretical and computational models. Good agreement has been achieved. The model validation of the non-ferromagnetic conductor has also done by comparing model predictions with existing benchmark experimental data. This numerical model can be used to refine the eddy current probe design and predict the probe signal due to cracks in ferromagnetic metallic parts.

A particular challenge of eddy current inspection in a fast reactor is that the coil position cannot be guided by optical aids due to the presence of liquid sodium during the periods when inspection is possible. However, electromagnetic sensing can be used. in the dissertation, we proposed a novel theoretical electromagnetic model of an eddy current probe with arbitrary orientation with respect to a tube or a plate. The experiment is also carried out and compared with theoretical prediction showing excellent agreement. The theoretical results are also useful in wobble noise analysis and the numerical method for fast evaluation of incident field term of integral equation method.

Copyright Owner

Tao Wu



File Format


File Size

214 pages